The twelve-tone, even-tempered system of Western music is the primary subject of traditional music education curriculum. Twelve musical tones are identified by the number of vibrations per second (vps) which cause a sound wave. The sound wave is heard as a musical tone (pitch).
The numeric scale of vibrations per second (vps) is a music industry standard to which musical instruments are calibrated to produce one or more sets of twelve musical sound waves. A musical sound wave is produced by some form of motion causing the musical instrument to vibrate. For instance, when a piano key is pressed down, a small hammer head strikes a group of piano strings inside of the piano. A piano tuner technician tunes each set of piano strings to produce a specific number of vibrations per second when the hammer head strikes the piano strings. The number of vps the piano strings are tuned to produce is defined by the music industry standard scale of numeric vps.
In traditional music education curriculum, seven alphabetic symbols, A, B, C, D, E, F and G are assigned to seven of the twelve numeric vibrations per second in the music industry numeric scale of vps. In the operating system of traditional music education curriculum, the functional role of the seven alphabetic symbols is designated to represent the fixed identity of seven musical tones.
In traditional music education curriculum, the five additional numeric vps of the twelve-tone, even-tempered system of Western music are designated as being “sharps” (♯) or “flats” (♭) of the seven primary alphabetic designations. Thus, traditional music teaching systems utilize seventeen symbols to represent the fixed identity of twelve musical tones as the core foundation upon which the entire operating system of teaching is built.
Multiple sets of the twelve-tone system are created by doubling the number of vibrations per second of each sound wave in the set, or by decreasing the number of vibrations per second of each sound wave in the set by exactly half.
The individual musical tones in each set of twelve tones are said to be related to each other by the correlation between the number of vibrations per second which cause the sound wave (exactly double or exactly half). The correlation of the numeric vps relationship between the individual tones in each twelve-tone group is represented by the conventional alphabetic symbol. The alphabetic symbol designated as the fixed identity of the musical tone remains the same in each twelve-tone group.
In traditional music education curriculum, the core foundation of the system of teaching is built upon the functional role of the alphabetic symbol being equal to (or being the same as) the functional role of the numeric vps as the fixed identity of the individual musical tone. In other words, the relationship between the alphabetic symbol and the numeric vps is reciprocal. Both symbols function as the fixed identity of the musical tone in the twelve-tone system of Western music. The functional role of the alphabetic symbol as the fixed identity of a musical tone is derived from the original equation where a unique alphabetic symbol is assigned to each of seven sound waves in the numeric scale of vps, for example, A=440 vps.
In the operating system of traditional music education curriculum, the functional role of the alphabetic symbol as the fixed identity of a musical tone is integrated into the curriculum by assigning the alphabetic symbol to the fixed identity of the lines and spaces of the musical staff, and to the different parts of musical instruments used to produce the individual musical tones, for example, the white and black keys of the piano.
In traditional music education curriculum, the term “music scale” refers to a collection of musical pitches (tones) arranged in order from lowest to highest or from highest to lowest.
In traditional music education curriculum, the music scale referred to as a “major” scale refers to a collection of seven musical pitches.
A system of numeric symbols, traditionally seven roman numerals, are assigned to designate the order in which the musical pitches occur in the collection of musical pitches referred to as the music scale.
The numbered position of the individual musical pitch within a music scale is referred to as the “scale degree.”
In traditional music theory curricula referring to Western music tonality, each pitch of a music scale is considered to function in a particular way with respect to the others. Therefore, scale degrees are both numbered (traditionally with roman numerals) and named, as follows: I=tonic, II=supertonic, III=mediant, IV=subdominant, V=dominant, VI=submediant, and VII=leading tone or subtonic.
In the traditional music education operating system, the “C major scale” consists of the following order of seven musical pitches: C, D, E, F, G, A, and B.
In the C major scale, the musical pitch C is placed in the first degree of the music scale referred to as the tonic. The musical pitch D is then placed in the second degree of the scale referred to as the supertonic. The musical pitch E is in the third degree of the scale referred to as the mediant. The musical pitch F is in the fourth degree of the scale referred to as the subdominant. The musical pitch G is in the fifth degree of the scale referred to as the dominant. The musical pitch A is in the sixth degree of the scale referred to as the submediant, and the musical pitch B is in the seventh degree of the scale referred to as the leading tone or subtonic.
In the music scales taught by traditional music education curricula, the alphabetic symbol which identifies the musical pitch in the music scale is represented to be equal to the numeric symbol of the scale degree.
For example, in the C major scale, C=1, D=2, E=3, F=4, G=5, A=6, and B=7
When the alphabetic symbol representing the fixed identity of the musical pitch placed in the first degree of the music scale is changed, the entire set of alphabetic symbols representing the fixed identity of the collection of musical pitches in the subsequent scale degrees also change.
For example, in the D major scale, D=1, E=2, F♯=3, G=4, A=5, B=6, and C♯=7.
In the G major scale, G=1, A=2, B=3, C=4, D=5, E=6, and F♯=7.
In the A major scale, A=1, B=2, C♯=3, D=4, E=5, F♯=6, G#=7.
As previously stated, the operating system of traditional music education curricula utilizes seventeen different symbols, A, A♯, B♭, B, C, C♯, Db, D, D♯, E♭, E, F, F♯, G♭, G, G♯, and A♭ to identify twelve musical tones, any one of which may be placed in the first scale degree of a major scale, thereby generating seventeen different possible orders of seven alphabetic symbols used to represent the tonal relationship of a collection of musical pitches defined by the musical term “major scale.”
In the conventional operating system of traditional music education curricula, the numeric designations function as a system of reference to a constantly changing set of alphabetic symbols used to identify the individual components of musical terms.
In the operating system of traditional music education curriculum, music chords are formed by selecting three or more musical pitches from a music scale to be played simultaneously.
In traditional music education curriculum, the musical term “I chord” refers to the fixed alphabetic identity of each of the three musical pitches which occupy the 1st, 3rd and 5th positions of a major scale. The “I chord” is understood to be equal to 1, 3 and 5 of the major scale. The three numeric symbols, however, are a reference to three unique alphabetic symbols representing the fixed identity of three musical tones.
In the key of C where C is equal to I, the three musical tones which the musical term “I chord” refers to, located in the 1st, 3rd and 5th positions of the C major scale, are identified as C, E and G.
In the key of G, where G is equal to I, the three musical pitches which the musical term “I chord” refers to, located in the 1st, 3rd and 5th positions of the G major scale, are identified as G, B and D.
In the key of A, where A is equal to I, the three musical pitches which the musical term “I chord” refers to, located in the 1st, 3rd and 5th positions of the A major scale, are identified as A, C♯, and E.
In the operating system of traditional music education curriculum, the term “I chord” referring to the musical pitches which occupy the positions 1, 3 and 5 of a music scale, refers to a constantly changing set of alphabetic symbols representing the fixed identity of the individual components of a three-tone cluster of musical pitches. In the conventional operating system of traditional music education curriculum, the three musical pitches of the I chord which occupy the 1st, 3rd and 5th positions of a major scale are dependent on the alphabetic symbol which identifies the musical pitch placed in the first position or tonic of the music scale.
The functional role of the numeric symbols in the operating system of traditional music education curriculum is derived from and is therefore directly linked to the core foundation of the operating system which defines the functional role of the alphabetic symbol as the fixed identity of the musical pitch the numeric symbol represents.
The functional roles of the alphabetic and numeric symbols in the operating system of traditional music education curriculum produce massive amounts of information necessary to comprehend the tonal relationship components of musical terms.